Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
5
,
No
. 2, Oct
o
ber
2
0
1
4
,
pp
. 15
3~
16
5
I
S
SN
: 208
8-8
6
9
4
1
53
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Direct
T
o
rque Control of
Four S
w
itch Th
ree Ph
as
e In
vert
er
Fed Induction Motor Sensorless Speed Drive
M. K. Me
tw
al
ly
Departement of
Electrical Eng
i
n
eering
,
Menouf
iy
a Univ
ersity
, Faculty
of
Engin
e
ering, Menoufiya,
Eg
y
p
t
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Feb 18, 2014
Rev
i
sed
Ju
l
20
,
20
14
Accepted Aug 15, 2014
This paper pr
es
ents sensorless speed con
t
rol of
induction
motor (IM) using
four switch thr
e
e phase
inverter
(FSTP
I) with direct torqu
e
and
flux contro
l
(DTFC). The p
r
oposed sensorless DTFC
sy
stem consists of an adaptiv
e
obs
erver of rotor flux to accu
rate
l
y
es
tim
ate
s
t
ator res
i
s
t
an
ce
and s
p
eed
simultaneously
, without
affecting dr
iv
e p
e
r
f
ormances.
The switching
techn
i
que for DTFC of IM usin
g FSTPI
in low
power applicatio
n is based on
the princip
l
e of sim
ilarit
y
betwe
e
n FST
PI and
SSTPI (six
switch three phas
e
invert
er), wher
e
the
αβ
plan is divided in
to 6 sectors and the form
ation of
the
voltag
e
space vector is done
in th
e same
way
as f
o
r SSTPI by
using effectiv
e
(mean) vectors. This
a
pproach
allows using th
e well-known estab
lished
switc
hing
ta
ble
of SST
PI for FST
PI.
T
h
e
sim
u
la
t
i
on resul
t
s indi
c
a
tes
that
th
e
sensorless speed control of FSTPI fed
IM with DTFC and adaptive observer
provides accu
rat
e
estim
ate
,
good
traje
c
tor
y
tr
acki
ng with differen
t
d
y
n
a
m
i
cs
performance. The experimental results
verif
y
the effec
tiven
ess of the
proposed metho
d
at diff
erent op
erating poin
t
s.
Keyword:
Ada
p
t
i
v
e fl
u
x
obs
er
ver
Di
rect
t
o
rq
ue
a
n
d
fl
ux
co
nt
r
o
l
Four
switch three phase i
nve
rt
er
I
ndu
ctio
n m
o
to
r
Sens
orl
e
ss
sp
e
e
d c
ont
rol
Stato
r
resistan
ce
id
en
tification
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
M. K. Metwally,
Departem
ent of Elect
ri
cal
Engi
neeri
ng,
M
e
no
ufi
y
a
Uni
v
ersi
t
y
, Fac
u
l
t
y
of
En
gi
nee
r
i
n
g
,
M
e
no
ufi
y
a, Eg
y
p
t
.
Em
ail: m
ohkam
e
l2007@ya
hoo.com
1.
INTRODUCTION
In
recent years significant advances have
been m
a
de on the sensorless
control of IM. One of the
m
o
st
wel
l
known m
e
t
hods used for cont
rol
of AC
dri
v
es
i
s
t
h
e Di
rect
Torque C
ont
rol
(DTC
). DTC
of IM
i
s
known t
o
have
a si
m
p
l
e
cont
rol
st
ruct
ure
wi
t
h
com
p
arabl
e
perform
ance t
o
t
h
at
of
t
h
e fi
el
d-ori
e
nt
ed
cont
rol
(FOC) techniques.
Unlike FOC
m
e
thods
, DTC
techniques require
utilization
of hysteresis
band com
p
arators
instead of
flux and
torque controlle
rs. To
replace the
coordinate transf
orm
a
tions and
pulse
width
m
odulation
(PW
M
) si
gnal
generat
o
rs of
FOC
,
DTC
uses l
ook-up
t
a
bl
es t
o
sel
ect
t
h
e
swi
t
c
hi
ng procedure
based on t
h
e
inverter states [1].
Direct torque
control (DTC)
of
induction
m
o
tors requires
an accu
rate knowledge
of the m
a
gnitude
and angular position of the controlle
d flux. In DTC, the flux is conve
ntionally obtained from
the
stator
voltage
m
odel, using the m
easured stator voltage
s and
currents. This m
e
t
hod, utilizes open loop pure
i
n
t
e
grat
i
on sufferi
ng from
t
h
e wel
l
known probl
em
s of i
n
t
e
grat
i
on effect
s i
n
di
gi
t
a
l
sy
st
em
s, especi
al
l
y
at
l
o
w
speeds operat
i
on range.
To obt
ai
n t
h
e
si
m
p
l
e
, effect
i
v
e perform
ances,
fast
cont
rol
of
t
o
rque and fl
ux;
a DTFC
sy
st
em
for
FSTPI-IM
has been proposed [2]
.
In t
h
i
s
paper,
t
h
e opt
i
m
al
swi
t
c
hi
ng l
ook-up t
a
bl
e i
s
est
a
bl
i
s
hed wi
t
h
four
basic
space vectors of
FSTPI and in
accord
ing with four
m
a
in sectors in
the
αβ
pl
an.
C
o
m
p
ari
s
on wi
t
h
DTFC
of i
nduct
i
on m
o
t
o
r fed by
convent
i
onal
SSTPI confi
r
m
t
h
at
FSTPI
t
opol
ogy
can be al
t
e
rnat
i
v
e t
o
t
h
e
convent
i
onal
t
opol
ogy
for l
o
w
power l
o
w
cost
i
nduct
i
on m
o
t
o
r
dri
v
es. DTFC
m
e
t
hod for
SSTPI-IM
has been
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16
5
15
4
i
m
proved
i
n
som
e
researches [3-10]
,
whi
l
e
t
h
e t
o
rque
and
speed ripples are reduced.
In order to reduce the
speed (torque) ripple, the space vect
or m
odulation (SVM) m
odul
ator has been used as shown in [5-9].
The
swi
t
c
hi
ng t
echni
que for DTFC-FSTPI-IM
i
n
t
h
i
s
paper has been done by
usi
ng t
h
e new
approach based on t
h
e pri
n
ci
pl
e
of si
m
i
l
a
ri
t
y
bet
w
een FSTPI
and SSTPI [5]
,
where
t
h
e
αβ
pl
an i
s
di
vi
ded
into 6 sectors and the form
ation of
the required reference voltage space vect
or is done in the sam
e
way as
for
SSTPI by using effective (m
ean) vectors.
In
the last decade, m
a
ny research
es
have been carried on the
design
of sensorless control schem
e
s of
t
h
e IM
. M
o
st
m
e
t
hods are basi
cal
l
y
based on t
h
e
M
odel
R
e
ference Adapt
i
v
e
Sy
st
em
schem
e
s (M
R
A
S)
[8]
.
Th
e b
a
sic MRAS
alg
o
r
ith
m
is v
e
ry
sim
p
le b
u
t
its
g
r
eatest d
r
awb
ack
is
th
e sen
s
itiv
ity to
u
n
certain
ties in
th
e
m
o
tor param
e
ters.
Another m
e
thod
ba
sed on
the Extended
Kalm
an Filter
(EKF) algorithm
is used
[12-14].
The EKF is a stochastic state
observer where nonlinear
equations are
linearized in every sam
p
ling period.
An
in
terestin
g
featu
r
e o
f
th
e
EKF is its
ab
ility to
estim
ate sim
u
ltan
e
o
u
s
ly
th
e states an
d
th
e p
a
ram
e
ters o
f
a
dy
nam
i
c
process. Thi
s
i
s
general
l
y
useful
for bot
h t
h
e
cont
rol
and t
h
e di
agnosi
s
of t
h
e process. In [14]
t
h
e
au
th
o
r
s u
s
ed
th
e EKF alg
o
r
ith
m
to
sim
u
ltan
e
o
u
s
ly estim
ate v
a
riab
les an
d
p
a
ram
e
ters o
f
th
e IM in
h
ealth
y
case and under di
fferent
IM
faul
t
s
.
[11]
used t
h
e Lu
enberger Observer
for st
at
e est
i
m
at
i
on of IM
.
The
Ex
ten
d
e
d
Lu
en
b
e
rg
er Ob
serv
er (ELO) is a d
e
term
in
istic
observer which also linearizes
the equations in every
sam
p
ling period. There is other type
of m
e
thods for state
estim
ation
that
is based on the intelligent techniques
[8]
.
The proposed sensorl
e
ss
DTFC
for
FSTPI fed
IM
showed
a good
behavi
or i
n
t
h
e t
r
ansi
ent
and
steady
st
at
es, wi
t
h
an excel
l
e
nt
di
st
urbance
reject
i
on of t
h
e
l
o
ad t
o
rque. Si
m
u
l
a
t
i
on
and experi
m
e
nt
al
resul
t
s
dem
onst
r
at
e
the effectiveness
of the
proposed control
over different
operating
conditions, a precise
estim
atio
n
in
lo
w
speed regi
ons i
s
obt
ai
ned.
2.
Space
Vec
t
or An
al
ysi
s
of
FS
T
P
I
Accordi
ng
t
o
t
h
e schem
e
i
n
Fi
gure
1 t
h
e swi
t
c
hi
ng st
at
us i
s
represent
e
d
by
bi
nary
vari
abl
e
s S
1
to
S
4
,
wh
ich
are set to
"1
" wh
en
th
e switch
is clo
s
ed
an
d
"0
" when open. In addi
t
i
on t
h
e swi
t
c
hes i
n
one
i
nvert
er
branch are controlled com
p
lem
e
ntar
y
(1 on, 1 off), therefore:
1
2
1
S
S
(1)
1
4
3
S
S
Phase t
o
com
m
on poi
nt
vol
t
a
ge depends on t
h
e t
u
rni
ng off si
gnal
of t
h
e swi
t
c
h as i
n
(2):
2
)
1
2
(
1
dc
ao
V
S
V
2
)
1
2
(
3
dc
bo
V
S
V
0
co
V
(2)
C
o
m
b
i
n
at
i
ons of
swi
t
c
hi
ng S
1
-S
4
result
in 4
general space
vectors
4
1
V
V
(Fi
g
.2, Tabl
e
1), com
ponent
s
αβ
of
t
h
e vol
t
a
ge vect
ors are gai
n
ed from
abc vol
t
a
ges usi
ng C
l
ark'
s t
r
ansform
a
t
i
on as i
n
(3):
c
b
a
V
V
V
V
V
2
3
2
3
0
2
1
2
1
1
3
2
(3)
W
h
ere V
a
, V
b
, V
c
:
out
put
vol
t
a
ges on t
h
e l
o
ad st
ar connect
i
on, defi
ned by
:
)
2
(
3
1
bo
ao
a
V
V
V
)
2
(
3
1
ao
bo
b
V
V
V
)
(
3
1
bo
ao
c
V
V
V
(4)
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4
Di
rect
T
o
rq
ue C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h Th
ree Ph
as
e In
verter
fed
Indu
ctio
n Mo
to
r
…
(M. K.
Metwa
lly)
15
5
Figu
re
1.
P
o
we
r circ
uit o
f
F
S
T
PI
Figure 2. Voltage s
p
ace vector of
FST
PI in the
αβ
plan.
Table 1. Co
m
b
inat
ion of
switching a
nd voltage space vectors
S1 S3
jV
V
V
0 0
3
2
1
3
j
dc
e
V
V
1 0
6
2
3
2
j
dc
e
V
V
1 1
3
3
3
j
dc
e
V
V
0 1
6
5
4
3
2
j
dc
e
V
V
To
si
m
u
l
a
t
e
si
x non-zero
vect
ors i
n
SSTPI,
besi
de t
h
e t
w
o
V
1
and V
3
,
it can be
used the effective vectors
V
23M
, V
43M
, V
14M
and V
12M
. These vectors are form
ed as follows:
;
3
)
(
2
1
0
3
2
23
j
dc
M
e
V
V
V
V
(5)
;
3
)
(
2
1
3
2
3
4
43
j
dc
M
e
V
V
V
V
;
3
)
(
2
1
4
1
14
j
dc
M
e
V
V
V
V
;
3
)
(
2
1
3
2
1
12
j
dc
M
e
V
V
V
V
To sim
u
late zero vectors of SSTPI, use the effective V
0M
as in (6):
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16
5
15
6
)
(
2
1
3
1
0
V
V
V
M
(6)
The sim
ilarity between space vector
s of FSTPI Fig.3 and SSTPI Figure 4 is presented in Table 2.
Figure
3. Voltage s
p
ace
vectors for (FST
PI)
on the
principl
e of sim
i
larity
Figure 4.
Base space vectors
i
n
SSTPI
Table 2. Simila
rity
betwee
n
s
p
ace vect
ors
of
FSTPI a
n
d SSTPI
Used voltage space vectors f
o
r
SSTPI
Used voltage space vectors f
o
r
FSTPI
V1 V23M
V2 V3
V3 V43M
V4 V14M
V5 V1
V6 V12M
V0,V7 V0M
3.
Modified
Switching Tec
hnique for
DTC
The object
i
v
e of t
h
e DTC
i
s
t
o
keep t
h
e m
o
t
o
r t
o
rque and st
at
or fl
ux wi
t
h
i
n
a defi
ned band of
tolerance by selecting
the m
o
st convenient
voltage sp
ace
vector from
(switching
table). In the
case of
the
convent
i
onal
swi
t
c
hi
ng t
a
bl
e of DTC for FSTPI-IM
, one of
four act
i
v
e vect
ors i
s
chosen (Tabl
e
3) [15]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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4
Di
rect
T
o
rq
ue C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h Th
ree Ph
as
e In
verter
fed
Indu
ctio
n Mo
to
r
…
(M. K.
Metwa
lly)
15
7
Tabl
e 3.
C
o
n
v
e
n
t
i
onal
swi
t
c
hi
ng
t
a
bl
e fo
r D
T
C
co
nt
r
o
l
m
e
tho
d
Δψ
Δ
T
Sector
1
-
240
0
+330
0
Sector
2
30
0
+60
0
Sector
3
60
0
+150
0
Sector
4
150
0
+240
0
1 1
V2
V3
V4
V1
1 -1
V1
V2
V3
V4
0 1
V3
V4
V1
V2
0 -1
V4
V1
V2
V3
In order to
reduce the
torque and speed
ripples by
using the principle
of sim
ilarity
for voltage
space
vect
ors, opt
i
m
um
swi
t
c
hi
ng t
a
bl
e
i
n
t
h
e m
odi
fi
ed
m
e
t
hod i
s
est
a
bl
i
s
hed si
m
i
l
a
rl
y
for t
h
e SSTPI
swi
t
c
hi
ng
table. The
αβ
plan
is divided in to
six s
ectors, and for
each sector, the
optim
al
space vector is chosen
accordingly
to the
required torque and
flux by using
the effective vectors
(equations 5, 6).
These vectors are
synthesized using the basic space vect
ors
with the duty cycle of 50%
(sw
itching period is Ts). The sam
e
way
is done for effective zero space vector (Table 4).
Tabl
e
4. M
odi
f
i
ed s
w
i
t
c
hi
n
g
t
a
bl
e f
o
r
D
T
C
c
ont
rol
m
e
t
hod
Δψ
Δ
T
Sector
I
-3
0
0
+30
0
II
30
0
+90
0
III
90
0
+150
0
IV
150
0
+210
0
V
210
0
+270
0
VI
270
0
+330
0
1
1 V
3
V
43M
V
14M
V
1
V
12M
V
23M
-1
V
12M
V
23M
V
3
V
43M
V
14M
V
1
0 V
13M
V
13M
V
13M
V
13M
V
13M
V
13M
-1
1 V
43M
V
14M
V
1
V
12M
V
23M
V
3
-1
V
1
V
12M
V
23M
V
3
V
43M
V
14M
0 V
13M
V
13M
V
13M
V
13M
V
13M
V
13M
The fl
ux and t
o
rque cal
cul
a
t
i
ons rem
a
i
n
t
h
e sa
m
e
. The stator flux is estim
ated as follows:
s
s
s
s
s
s
T
R
i
v
)
(
0
(7)
s
s
s
s
s
s
T
R
i
v
)
(
0
The estim
ated stator flux
s
~
and fl
ux angl
e sect
or are defi
ned as fol
l
o
ws:
s
s
i
s
s
s
arctan
;
~
2
2
(8)
Th
e to
rq
u
e
is estim
ated
b
y
th
e fo
llo
win
g
fo
rm
u
l
a:
s
s
s
s
i
i
P
T
2
3
~
(9)
W
h
ere:
v
s
,i
s
St
at
or vol
t
a
ge and current
vect
ors
R
s
Stator resistance
P
Num
b
er of pol
e pai
r
T
El
ect
rom
a
gnet
i
c
t
o
rque
s
St
at
or fl
ux vect
or
T
s
Sam
p
lin
g
tim
e
4.
Ro
to
r spee
d,
Fl
ux
a
nd S
t
at
or
Resi
st
ance
E
s
ti
ma
ti
on
B
a
sed A
d
a
p
ti
ve
Obser
v
er
To defi
ne t
h
e adapt
i
v
e observer, st
at
or vol
t
a
ges
and currents are used to estim
ate the rotor flux (
ψ
r
),
speed (
ω
r
), and stator resistance (
R
s
) according to adaptation laws that m
u
st
ensure the stability of
the
system
.
C
onsi
d
er
t
h
en t
h
e speed and resi
st
ance
st
at
or as const
a
nt
param
e
t
e
rs and
unknown. The st
at
e equat
i
on of t
h
i
s
observer i
s
t
h
en expressed as fol
l
o
ws by
separat
i
ng t
h
e st
ate m
a
trix
in
two
,
o
n
e
fo
r th
e sp
eed
an
d
th
e
o
t
h
e
r
fo
r
stator resistance [16].
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l.
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.
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t
o
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e
r 201
4 :
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53 –
16
5
15
8
)
ˆ
(
ˆ
)
ˆ
(
)
ˆ
(
.
ˆ
s
s
s
Rs
r
r
i
i
K
BU
X
R
A
A
X
(10)
W
h
ere
5
4
5
4
2
3
11
3
2
11
ˆ
0
ˆ
0
ˆ
0
ˆ
0
)
ˆ
(
a
a
a
a
a
a
a
a
a
a
A
r
r
r
r
r
and
0
0
0
0
0
0
0
0
0
0
0
0
0
0
)
ˆ
(
6
6
s
s
s
R
a
R
a
R
A
K
i
s
t
h
e observer gai
n
m
a
t
r
i
x
whi
c
h governs t
h
e dy
nam
i
cs and t
h
e observer’s robust
n
ess;
i
t
i
s
cal
cul
a
t
e
d as
fo
llo
ws:
T
K
K
K
K
K
K
K
K
K
3
4
1
2
4
3
2
1
(11)
The coefficients
K
1
, K
2
, K3
, and
K
4
are defi
ned as fol
l
o
ws:
r
r
s
T
T
L
k
K
1
)
1
(
1
)
1
(
1
1
r
k
K
ˆ
)
1
(
1
2
r
r
s
r
r
s
T
T
L
a
k
T
T
L
a
k
K
1
)
1
(
1
.
)
1
(
1
)
1
(
1
)
1
(
3
1
3
2
1
3
r
a
k
K
ˆ
)
1
(
3
1
4
,
k
1
> 1
A
hat above a sym
bol in (10) de
notes estim
ated quantities, sym
bol
T
r
is th
e ro
to
r tim
e co
n
s
tan
t
,
L
s
st
at
or i
nduct
a
nce,
L
r
rot
o
r
i
nduct
a
nce and
l
eakage coeffi
ci
ent
)
/(
2
1
r
L
s
L
m
L
.
The coefficient
k
1
is
chosen
to im
pose a
dynam
i
c observer faster
than the
system
.
The speed adaptive
m
echani
s
m
can be deduct
e
d
by
t
h
e Ly
apunov t
h
eory
[17, 18]
.
If we choose an adequat
e
candi
dat
e
funct
i
on,
aft
e
r appl
i
cat
i
on of t
h
e Ly
apunov t
h
eory
, t
h
e
fol
l
o
wi
ng
adapt
a
t
i
on l
a
w for t
h
e speed i
s
got
t
e
n [17–19]
:
r
is
e
r
is
e
s
i
K
p
K
r
ˆ
ˆ
ˆ
(12)
W
h
i
l
e
t
h
e st
at
or resi
st
ance est
i
m
at
i
on i
s
gi
ven by
t
h
e adapt
a
t
i
on l
a
w defi
ned by
:
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8-8
6
9
4
Di
rect
T
o
rq
ue C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h Th
ree Ph
as
e In
verter
fed
Indu
ctio
n Mo
to
r
…
(M. K.
Metwa
lly)
15
9
s
i
is
e
s
i
is
e
s
iRs
K
pRs
K
s
R
ˆ
ˆ
ˆ
(13)
W
ith
s
i
s
i
is
e
ˆ
and
s
i
s
i
is
e
ˆ
W
h
ere
k
p
ω
,
k
I
ω
,
k
pRs,
k
IRs
, are
PI controller param
e
ters of roto
r speed and stator resistance adaptation
m
echanism
s
respectively.
The role of adaptive m
ech
an
ism
s
is to
m
i
n
i
m
i
ze th
e fo
llo
win
g
erro
rs
ε
ω
r
,
ε
RS
:
r
is
e
r
is
e
r
ˆ
ˆ
s
i
is
e
s
i
is
e
Rs
ˆ
ˆ
(14)
Finally, the value of speed and stator resistance can
be est
i
m
at
ed by
si
m
p
l
e
PI cont
rol
l
e
rs. The
norm
of rot
o
r fl
ux and i
t
s
posi
t
i
on are det
e
rm
i
n
ed by
t
h
e fol
l
o
wi
ng rel
a
t
i
ons:
2
ˆ
2
ˆ
ˆ
r
r
r
(15)
r
r
arctg
r
ˆ
ˆ
(16)
The rel
a
t
i
on bet
w
een rot
o
r fl
ux and st
at
or fl
ux as i
n
(17)
s
X
s
i
s
r
(17)
W
h
ere
X
s
is the stator reactance.
5.
Drive System
The
bl
ock di
agram
of IM
DTFC
dri
v
e
sy
st
em
wi
t
h
proposed
adapt
i
v
e observer
i
s
shown
i
n
Fi
gure 5.
The system
basically com
p
rises two
hy
st
eresi
s
cont
rol
l
e
rs for fl
ux l
i
nkage and t
o
rque cont
rol
,
t
h
ese
cont
rol
l
e
rs, i
n
conjunct
i
on wi
t
h
t
h
e m
odi
fi
ed swi
t
c
hi
ng
t
a
bl
e for FSTPI (Tabl
e
4) si
m
i
l
a
rl
y
for
SSTPI
swi
t
c
hi
ng t
a
bl
e, generat
e
t
h
e out
put
si
gnal
s
t
o
t
h
e gat
e
s of t
h
e power swi
t
c
hes of t
h
e i
nvert
er.
Usi
ng
t
h
e opt
i
m
um
swi
t
c
hi
ng
t
a
bl
e for FSTPI reduces
t
h
e t
o
rque and
speed ri
ppl
es. The i
nvert
er
u
s
ed
in
th
is system
is FSTPI.
Fi
gu
re
5.
B
l
oc
k
di
ag
ram
of I
M
DTFC
sy
st
em
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,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
53 –
16
5
16
0
Th
e ro
le o
f
th
e flu
x
co
n
t
ro
ller is to
m
a
in
tain
th
e flu
x
am
p
litu
d
e
with
in
a n
a
rro
w h
y
steresis
b
a
n
d
around t
h
e reference val
u
e
s
. The
torque controller receives the
inform
ation obtained from
the
torque
calculator
and com
p
ares this
va
lu
e with
th
e
referen
ce to
rq
u
e
T
*
(out
put
of a speed
PI cont
rol
l
e
r). Two current
sensors m
easure the m
o
tor
currents (
i
a
, i
b
) whi
l
e
a vol
t
a
ge sensor
m
easure t
h
e m
o
t
o
r vol
t
a
ges
(
v
a
, v
b
) th
at,
in
conjunct
i
on wi
t
h
swi
t
c
hi
ng t
a
bl
e, i
s
used t
o
com
put
e t
h
e st
at
or vol
t
a
ges (
v
s
α
, v
s
β
). The st
at
or fl
ux l
i
nkage
s
~
,
its angular position
i
and
estim
ated torque
T
~
are
given in
(7), (8),
(9). Al
so the
estim
ated speed
and stator
resi
st
ance are gi
ven i
n
(12), (13).
6.
Simulatio
n
Results
M
odel
i
ng
and si
m
u
l
a
t
i
on work
has been perform
ed t
o
exam
i
n
e t
h
e cont
rol
al
gori
t
h
m
of IM
DTFC
usi
ng m
odi
fi
ed swi
t
c
hi
ng t
a
bl
e for FSTPI based on adapt
i
v
e observer for rot
o
r fl
ux, speed and
st
at
or
resi
st
ance
est
i
m
at
i
on usi
ng M
A
TLAB
/
SIM
U
LINK
soft
ware. The param
e
t
e
rs
of t
h
e i
nduct
i
on m
o
t
o
r
prot
ot
y
p
e are l
i
s
t
e
d i
n
appendi
x I. The sam
p
l
e
peri
od
T
s
is 5
0
μ
s
and t
h
e l
o
ad t
o
rque
i
s
set
t
o
be
5.0 N.m
at
50
rpm
speed and also at zero speed during forward m
o
tori
ng
operat
i
on when t
h
e speed change t
o
-50 rpm
at
t
=
4sec t
h
e t
o
rque change t
o
-5.0 N.m
duri
ng reverse m
o
t
o
ri
ng operat
i
on.
In all sim
u
lations, the estim
ated speed was used
fo
r sensor-less speed control and the actual speed
is
present
e
d for com
p
ari
s
on purpose.
Fi
gu
re
6.
U
p
pe
r:
R
e
fere
nce
(
b
l
u
e),
est
i
m
a
t
e
d (re
d)
an
d act
ua
l
(bl
a
c
k
)
r
o
t
o
r
spee
d i
n
r
p
m
.
Lo
wer:
s
p
ee
d e
r
r
o
r
(r
pm
).
Fi
gure 6 shows
t
h
e speed waveform
s
under l
o
ad operat
i
on
when t
h
e sensorl
e
ss
speed cont
rol
was
perform
ed usi
ng t
h
e proposed m
e
t
hod for FSTPI
t
h
e speed change from
50 rpm
t
o
zero rpm
at
t
=
2sec
wi
t
h
load torque equal to 6 N.m
and
also the speed change fro
m
zero
rpm
to -50 rpm
at t=
4 sec as well as the
load
t
o
rque changes from
6 N.m
t
o
-6 N.m
i
n
t
h
e reverse m
o
t
o
ri
ng
operat
i
on. The speed
com
m
a
nd appl
i
e
d i
n
t
h
e
speed
cont
rol
l
e
r i
s
shown i
n
Fi
gure 6
upper di
agram
(bl
u
e)
i
n
revol
ut
i
on
per m
i
nut
e
(rpm
)
t
h
e est
i
m
at
ed
speed
(red) and the
actual rotor speed
(black). The difference
between th
e actual
speed and estim
ated speed
in rpm
is
shown in Figure
6 lower diagram
.
The resu
lts show
the accuracy of
th
e sensorless speed
control
duri
ng st
art
i
ng wi
t
h
l
o
ad operat
i
on as wel
l
as speed change operat
i
ons.
Fi
gure
7 upper di
agram
shows a com
p
ari
s
on bet
w
een
t
h
e act
ual
rot
o
r angl
e (bl
ack) and t
h
e
est
i
m
at
ed
rot
o
r angl
e
(red) duri
ng
t
h
e t
e
st
depi
ct
ed i
n
Fi
gure
6 al
so
Fi
g .7
l
o
wer di
agram
shows t
h
e l
o
ad
torque (red) and
the estim
ated torque
(black) in
N.m
.
The figures
show the accuracy
of the
proposed
t
echni
que.
Fi
gure 8
upper di
agram
s
shows t
h
e
act
ual
rot
o
r fl
ux
angl
e (bl
ack)
and t
h
e
est
i
m
at
ed rot
o
r fl
ux
angl
e (red), Fi
gure 8 l
o
wer di
agram
shows t
h
e error
be
tween the actual and estim
ated rotor flux angles
in
degrees for the
tests depicted
in Fi
gure
6. The
steady state error
is n
early zero
which indicates
that the
proposed m
e
thod of sensor-less speed c
ontrol is very accurate with zero
speed
error at very low speed as well
as zero speed under hi
gh l
o
ad operat
i
ons.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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208
8-8
6
9
4
Di
rect
T
o
rq
ue C
ont
r
o
l
of
Fo
u
r
Sw
i
t
c
h Th
ree Ph
as
e In
verter
fed
Indu
ctio
n Mo
to
r
…
(M. K.
Metwa
lly)
16
1
Fi
gu
re
7.
U
p
pe
r:
act
ual
rot
o
r a
ngl
e
(
b
l
ack)
,
es
t
i
m
a
t
e
d r
o
t
o
r a
ngl
e
(re
d
)
i
n
o
.
L
o
w
e
r
:
Lo
ad
to
rqu
e
(r
ed
)
and
esti
m
a
ted
to
rqu
e
(b
lack
) i
n
(N.m
).
Figu
re
8.
U
p
pe
r: actual
(blac
k
), estim
ated (re
d)
r
o
to
r fl
ux
an
gle in
o
. L
o
we
r
:
Err
o
r
bet
w
ee
n act
ual
an
d
esti
m
a
ted
ro
tor flux
ang
l
e in
o
.
Fi
gure 9 shows t
h
e m
o
t
o
r current
i
n
the
stationary
reference fram
e
(
α
,
β
) (upper di
agram
)
and
t
h
e
three phase m
o
tor currents Iabc (lower diagram
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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94
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PED
S
Vo
l.
5
,
No
.
2
,
O
c
t
o
b
e
r 201
4 :
1
53 –
16
5
16
2
Figu
re
9.
U
p
pe
r: m
o
tor cu
rre
n
t
in stationa
ry
r
e
fere
nce
fram
e
(
αβ
)
in
(A
).
L
o
we
r: m
o
tor c
u
rre
nts Ia
bc i
n
(
A
).
Figure 10:
actual
stator resistance (blac
k
-
dott
e
d) and estim
ated
stator resistance (re
d)
in
o
h
m
Fi
gu
re 1
1
. St
at
or
fl
u
x
l
i
n
ka
ge l
o
cus
i
n
(
W
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.